Review: Number Systems

Which of the following numbers is NOT rational?

• 5 ⅜

• 0

• π

• 6.0̅2

• √81

Which of the following numbers is NOT rational?

• √25

• ⅗

• -47

• √10

• 0.213̅4̅5̅

Round the following number to the nearest hundredth:

√28.066

• 5.30

• 14.33

• 5.98

• 7.22

• 9.03

Round the following number to the nearest tenth:

√1.579

• 1.5

• 0.7

• 0.5

• 1.2

• 1.3

 Which of the following expressions, when evaluated, equals an irrational number?

•  $\frac{\sqrt{2}}{\sqrt{8}}$  

•  $\frac{\sqrt{8}}{\sqrt{2}}$  

•  $\left(\sqrt{8}\right)^2$  

•  $\sqrt{2}\times\sqrt{8}$  

•  $\sqrt{2}+\sqrt{8}$  

What fraction lies exactly between 2/3 and 3/4?

• 3/5

• 5/6

• 7/12

• 9/16

• 17/24

If x > 1, then which of the following has the least value?

• $\sqrt{x}$

• $\sqrt{2x}$

• $\sqrt{x\ \cdot\ x}$

• $x\sqrt{x}$
  

• $x\cdot x$

 $\frac{5}{3}$   $\frac{7}{4}$   $\frac{6}{5}$   $\frac{9}{8}$ 

In what order should the following be listed to be arranged by increasing size? 

•  $\frac{9}{8}<\frac{6}{5}<\frac{5}{3}<\frac{7}{4}$ 
  

•  $\frac{9}{8}<\frac{6}{5}<\frac{7}{4}<\frac{5}{3}$  

•  $\frac{7}{4}<\frac{5}{3}<\frac{9}{8}<\frac{6}{5}$  

•  $\frac{6}{5}<\frac{9}{8}<\frac{5}{3}<\frac{7}{4}$  

•  $\frac{5}{3}<\frac{6}{5}<\frac{7}{4}<\frac{9}{8}$  

What of the following decimals has the greatest value?

• 0.5̅1̅5̅

• 0.̅1̅5̅

• 0.515

• 0.155

• 0.5

Which of the following numbers lies between  $-\sqrt{11}$  and  $-\sqrt{5}$  ?

• -8

• -6

• -4

• -3

• -1